Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

Question

Answer 1

y = 3(x-3) -2 = 3x -9-2 = 3x -11

y=3x-11 is a parallel line through (3,-2)

y = (-1/3)(x-3) -2 = -x/3 +1-2

y =-x/3 -1 is a perpendicular line through (3,-2)

or

x+3y = -3

parallel lines have the same slope = 3= the coefficient of the x term when solved for y

perpendicular lines have a negative inverse slope. change the sign and flip it upside down, from 3/1 to-1/3

3 = (y+2)/(x-3) is parallel

-1/3 = (y+2)/(x-3) is perpendicular

slope of the original line is "rise over" run, or have much y increases as x increases. 6/2 = 3

(1,-4) to (3,2) has the y coordinate change from -4 to 2 =6 and x coordinate correspondingly changed from 1 to 3 = 2. 6/2 = change in y coordinate divided by change in x coordinate. Look at the graph, those two points show the line going through them. tip of the top arrow points right at (3,2)